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OpenAI reports: Smooth isometric immersion of surfaces into four-space

OpenAI claims that every compact boundaryless smooth Riemannian surface has a smooth length-preserving immersion into R⁴, including nonorientable surfaces.

Sources for this record

What was already known

Smooth immersion into five-space and higher-dimensional embedding results provide different ambient-dimension baselines.

What changed and why it matters

Advances the stated target relative to the recorded baseline.

The AI contribution

OpenAI attributes the manuscript to its internal model; individual human contributions remain unspecified.

Limitations

Closed means compact without boundary. Self-intersections are allowed, so this is not a smooth isometric embedding theorem. Nonorientable surfaces are included. Preprint. AIProofWatch read the source statement and context; it has not refereed the proof, compiled a formal development, or established community acceptance.

Verification evidence

Evidence labels show what supports the claim. Importance rates its impact if correct.

Author claim

The original source reports this scoped result; AIProofWatch reviewed its statement, not the full proof.

Accessible artifact / proof

A research manuscript or proof artifact is publicly accessible; availability is not independent checking.

Correction and publication history